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Made-up problem

  1. Mar 10, 2007 #1
    I made up a problem and wanted to make sure that I did everything right.

    A thing rod with mass M is bent into the shape of a quarter circle with radius R. It is positioned so that it looks like the arc made as theta moves from terminal position (+ x axis) to 90 degrees counterclockwise. I am going to let this arc rotate freely about the x-axis. My problem is to determine the speed of the tip of the wire when it has rotated all the way to the bottom.

    First I calculated the potential energy of the rod using the x-axis as a refrence frame. I did this by integrating over the rod noting that the height of each piece is Rsin@

    U=(2/pi)MgR.

    Then I calculated the moment of inertia using the same integration techniques.

    I=(1/2)MR^2

    (Is that really true!?!?!)

    Finally I doubled the initial potential energy to get the kinetic when it has spun around and set that equal to (1/2)Iw^2

    v=4[gR/pi]^(1/2)

    If anyone would check this I would be very appreciative.
     
  2. jcsd
  3. Mar 11, 2007 #2
    Should I perhaps move this question to a different forum?
     
  4. Apr 2, 2007 #3
    define "thing rod"
     
  5. Apr 2, 2007 #4
    He means thin rod.
     
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